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De Schutter: Purkinje Cell Model

Effect of active membrane on the electrical properties of Purkinje cells


We have used the model to contrast the electrical properties of a passive Purkinje cell dendrite with those of a dendrite with the active properties just described. Figure 12 shows the effect of including voltage-dependent conductance on the electrotonic structure of the model. In this figure, Sholl diagrams [1] are presented in units of electrotonic length of the Purkinje cell under different conditions. At the right side, enlargements show the electrotonic lengths of a few distal branchlets in a passive membrane model (no active conductances in the model; Fig. 12B) and in an active membrane model during and after a dendritic spike. One can see that adding active membrane to the cell roughly doubled its electrotonic size during the resting state shown in Fig. 12C (the dendritic membrane had a potential of about -60 mV) and that during a dendritic spike the electrotonic size was roughly doubled again (Fig. 12D). The electrotonic distance from the soma to the marked dendritic tip (morphological distance 392 μm) was 0.57 λ in the passive model; it was 0.95 λ in the active model in the resting state and 1.57 λ in the active model during the dendritic spike.


[1]   DA Sholl. Dendritic organization in the neurons of the visual and motor cortices of the cat. Journal of Anatomy, 87:387–406, 1953.